import matplotlib.pyplot as plt

# 训练集
x_data = [1.0, 2.0, 3.0]
y_data = [2.0, 4.0, 6.0]

# 初始化权重
w = 1.0

# 定义线性拟合函数
def forward(x):
    return x * w

# 定义损失函数（均方误差）
def cost(xs, ys):
    cost = 0
    for x, y in zip(xs, ys):
        y_pred = forward(x)
        cost += (y_pred - y) ** 2
    return cost / len(xs)

# 定义梯度函数
def gradient(xs, ys):
    grad = 0
    for x, y in zip(xs, ys):
        grad += 2 * x * (x * w - y)
    return grad / len(xs)

# 存储迭代次数和损失函数
epoch_list = []
cost_list = []

print('predict (before training)：','x = 4','y=',forward(4)) #训练之前：预测

# 梯度下降算法
for epoch in range(100):
    cost_val = cost(x_data, y_data)
    grad_val = gradient(x_data, y_data)
    w -= 0.05 * grad_val  # 0.01 learning rate
    print('epoch:', epoch, 'w=', w, 'loss=', cost_val)
    epoch_list.append(epoch)
    cost_list.append(cost_val)

print('predict (after training)：','x = 4','y =',forward(4)) #训练之后：预测

# 可视化
plt.plot(epoch_list, cost_list)
plt.ylabel('cost')
plt.xlabel('epoch')
plt.show()